2014 November 22

A couple of weeks ago, Peter Sipe published an article How to challenge voracious young readers, in which he talked about famous authors who were anti-school (Thomas DeQuincey, W. Somerset Maugham, George Orwell, Roald Dahl, Morrissey, …). He points out that these authors may well have been autodidacts:

Which brings me back to the question of how I can make a difference for my gifted students. What these authors wrote about school does offer guidance. I find it instructive that they seem to have gained their erudition despite school, not because of it. Accordingly, I don’t think young DeQuincey et al. would much need a sixth-grade reading teacher.

But perhaps they could use a helpful librarian.

I think that it is very difficult for the average teacher in the US to make much difference for a gifted student—they don’t have the time, the training, the desire, nor (in some cases) the intelligence to inspire the gifted students. And their job, as set down by the administration and the politicians, is to get the slowest students up to minimal standards, not to help the gifted students move ahead more rapidly. In fact, many politicians and educrats would prefer it if the teachers held the gifted students back from learning, so that all students were performing at exactly the same level, doing exactly the same things. (A lot still haven’t gotten the message that equitable education doesn’t mean giving every student exactly the same lesson at the same time.)

The notion of turning over a lot of the education of gifted students to books is not a bad one—and a good librarian can recommend books to students more easily than a teacher can make up worksheets. A lot of gifted students would benefit more from reading books that are in their “zone of proximal development” than from doing classroom exercises that practice skills they mastered years earlier or from playing teacher’s helper and trying to explain stuff that it obvious to them to kids who really need help from those trained in content pedagogy.

But there are limits to what one can learn from books alone—there are skills that require practice to perfect, and reading about them is not the same thing as practicing them. The hard part with teaching gifted students is in providing them with appropriately challenging problems that will exercise and improve their skills without boring them or frustrating them too much. Finding appropriate problems is a major challenge for teaching any student, but for students clustered near the middle of the range that teachers teach, there are a lot of materials already prepared, and teachers have been well-trained to recognize and address those students’ needs. School districts have to provide specially trained special-ed instructors for students who are way behind the average, but they generally do little or nothing for those who are more advanced.

I think that the fields that have succeeded best at providing materials for challenging gifted students are mathematics (Project Euler and the courses and books from Art of Problem Solving, for example), computer programming (lots of different paths for getting into programming), and engineering (especially with the current popularity of the Maker movement and various robotics team projects). Students can also progress fairly easily to adult levels in reading, since books at all levels are widely available, but there isn’t much for getting practice in humanities fields, nor social sciences, or even most of the physical and biological sciences. Students interested in those fields may have to remain content with being autodidacts, and just reading about their fields, at least until they get into college (and sometimes until they get into grad school).

I don’t think schools in general do a very good job of teaching gifted students, but giving them unfettered access to a good library is one way to undo the damage caused by the schooling. Adding in access to challenging problems and tools for making things (with mentors to help them learn to use the tools) could turn the rather dismal current (lack of) education for gifted children into something really productive of learning. Of course, the same access can and should be given to other students, though few will make much use of the library.

2013 August 8

Hard Math for Elementary School by Glenn Ellison: (ISBN 9781489507174) looks like a book I could have used with my son about 8 years ago (too bad it was just published a couple of months ago).

The premise is simple: it is a math enrichment textbook, intended to take the topics of elementary school math deeper for gifted students.

The presentation is good, but the students will have to be reading at the 4th grade level as well as doing math at that level to get much out of the book. This is not a flashy book with lots of illustrations and stories—it is just cool math, presented as cool math.

Disclaimer: I don’t have a copy of the book, and I haven’t read much of it. I used Amazon’s “Look Inside” feature to look at the table of contents and a couple of pages, and saw such gems as calculation tricks for computing some squares (like 552=3025) quickly. (The trick is based on , but the author wisely avoids algebraic notation.)

I suppose that getting something designated as “National x Week” makes the people who argue for it feel like they’ve accomplished something, though it has never been clear to me exactly what. Since there are so many “National x Weeks” it buys you no publicity, unless you have events scheduled all over the country simultaneously (like with National Bike Month and Bike-to-Work Week). Incidentally, that event started as a number of local celebrations that gradually coalesced into a national movement that the League of American Bicyclists and other existing bike advocacy organizations joined—the locally run events are still the mainstay of the activity, though there are multiple efforts to try to coordinate them (not just LAB, but also biketoworkinfo.org).

National Engineers Week is trying to get engineering schools and faculty to put on events, but without a lot of success, because they chose a poor week for faculty or student involvement entirely for political reasons. (Bike-to-Work week, in contrast, was chosen as a compromise between the various “beginning of the cycling season” dates around the country.)

National Parenting Gifted Children Week has no special activities (other than a blog tour that was not mentioned on any of the several parents-of-gifted-kids mailing lists that I read, so probably only reached the people who already read those blogs). Unfortunately, this sort of feeble, invisible PR effort seems to be typical of organizations like NAGC and SENG. I’m sure that they mean well, but I can’t see enough positive results from their efforts to want to join the organizations. There are 1000s of well-meaning organizations that want my time and money (and dozens who send me requests). I’d rather support organizations that seem to be efficient and effective (like Second Harvest Food Bank and Planned Parenthood), even if I have no expectation of ever having any use for their services.

In this speech to teachers of Advanced Placement courses, Dr. VanTassel-Baska argues that AP courses are critical for gifted students, as a means of differentiating instruction for them. She said things like

In the late 1970’s gifted students reported AP to be the most beneficial program taken during their high school years. This perception has not changed appreciably over the intervening decades (Kolitch & Brody, 1992).

Of course, since she gave the talk in 2000, there has been a big push to get more students into AP courses, so that many of the courses are no longer all that suited for gifted kids. Even at that time, she pointed out

One issue that Advanced Placement teachers need to be aware of is the different levels of aptitude for a particular AP course. The range of ability in AP classes is typically very great. Even if all students were identified as gifted, the range would be as broad as in heterogeneous classes. Such differences in aptitude level require more attention to addressing individual needs. Because AP course work probes depth of understanding, it tends to reveal greater disparity in student learning. Level of aptitude may predict how much material students can handle well, how capable they are to work independently, and how strong they are conceptually with the material. Use of various forms of flexible grouping for in-class work may be an antidote to this problem. Organizing sections of AP by ability levels may also be useful in subjects where enrollments are sufficiently high.

The trend to lower the barrier to entry for AP courses over the last decade has made this problem worse. The teaching strategies that are most effective for the bottom half of a current AP course may be quite unsuitable for the kids in the top quarter, who don’t need many routine practice problems, but rather a smaller number of more challenging questions that stretch their minds.

While AP courses may still be the best option available to most gifted high school students, many need to look elsewhere for teaching at their level. Community college courses sometimes provide this, though that varies enormously, as many community college courses are intended to remediate inadequate high school preparation for college, and may be taught in an even less suitable way for gifted students than AP courses.

Sometimes sufficient challenge can be found by skipping prereqs—the review built into the beginning of most courses can serve as a fast-paced introduction to the material for a gifted student. This is essentially what we did by teaching my son a course that covers AP Physics C: Mechanics, with no previous physics courses. He had picked up almost everything from a conceptual physics course by reading various popular books about physics, and his math was strong enough that he did not need the crutch of algebra-based physics, but could jump right into calculus-based physics. (Actually, I think that calculus-based physics is somewhat easier, if you have the math, since there are fewer formulas to memorize—a lot can be trivially rederived from the definitions of force as the derivative of momentum with respect to time and of potential energy with respect to displacement, for example.)

I think that one problem with AP classes as a primary means of teaching gifted high school students is an extension of a common problem in gifted education in lower grades: what the students need is work that is more complex and sophisticated, not more work. Too many AP courses pile on drudgery, in the mistaken belief that this makes them more like college courses. (See my analysis in How many AP courses are too many?) This overload of marginally useful work prevents them from taking on more independent, non-curricular projects (like science fair, debate, theater, or internships) from which they would actually learn more.

I’m not saying that I think that AP courses are a bad idea, nor that gifted students should avoid them. There are times when an AP course is precisely what a gifted student needs and other times when it is the best available choice. Taking AP courses is one of many ways for gifted students to learn, just not always the best way.

There are several reasons we’ve been reluctant to use many on-line courses:

Many are quite expensive. EPGY courses are around $500 to $750, plus $50 registration and shipping fees, JHU-CTY courses are $500–$1280. I’d want to know that the course would be a very good fit and of higher quality than a corresponding community college class (about $300) before committing to an online course.

Too much screen time. My son already spends more time in front of a screen than is healthy (as do I, so I can’t chide him too much). At least with community college classes he gets the exercise of bicycling to the class (in fact, this provides so much exercise that it counts as his PE class: about 4 hours a week).

Difficulty in finding courses that fit his educational needs and interests. There are undoubtedly a number of courses that would be an excellent fit for him, but it is very difficult to distinguish them from other courses that have similar descriptions but would be at the wrong pace, wrong level, or have too much busy work.

So far we have only used one on-line course provider: Art of Problem Solving. A year ago, I posted about our experience with with their precalculus course: Good online math classes. My son did their calculus class this year with the same instructor, and we had similarly good results. The AoPS calculus classes are not cheap ($500 with books), but they were an excellent fit for my son. If I could be assured of as good a fit in other online courses, I would be more willing to use online providers.

This year my son has been keeping time logs for his consultant teacher in the home-school umbrella. For the AoPS calculus class that just ended, he did almost all the weekly and challenge problems, but not quite all. We added up the total hours (class and homework) for February and March, and got 56 hours—just under 7 hours a week. His total workload for all courses (including the cycling that counts as PE) averaged 40.75 hours a week in February, which I regard as about the right amount of time for a high school student to be spending on school. It is certainly much larger than the 2–3 hours a day that some home schoolers regard as adequate. The main advantage for us of home schooling is not a reduction in workload, but a spending the time on appropriate work, rather than busy work or dead time.

I think that the calculus class was a good deal higher workload than the Precalculus class last year, but we did not keep time logs then, so I may be mistaken. My son did not take any of their lower-level classes, so I can’t comment on the workload of any of them (though we did use the intro algebra and intro geometry books some earlier, and were happy with them, which is why I was willing to give AoPS online courses a chance).

My understanding is that by the end of the AoPS calculus course well over half the students had dropped, possibly because they could not keep up with the pace or the workload. You only get your money refunded if you drop in the first 3 weeks, so a lot of families ended up wasting the tuition money. I’m afraid of a similar thing happening if we pick an online course that is not a good fit for our son.

He will probably do one AP practice test before taking the AP Calculus BC test next month, but that should only take about 3.5 hours. The AP test should be a good review of the essential material of the course, but so far as I can tell, the AoPS Calculus class covers more material in greater depth than the usual AP calculus BC course or the usual first-year college calculus class. It is definitely a calculus-for-mathematicians course, with a lot of emphasis on problem solving and rigorous foundations (like using Darboux integrals, a somewhat cleaner equivalent to Riemann integrals). Some of the differential and integral equations they had in the last challenge set seemed difficult even for me (though I must admit that ODE was never my favorite subject, and it has been over 30 years since I last did any differential equation other than a trivial exponential decay).

The AoPS courses also cover complex numbers fairly well, something that is not always done in other precalculus and calculus classes. Another gifted high school student I know has taken calculus through multi-variable calculus at the local community college. I was amazed to find out that he’d had almost nothing about complex numbers: not even such fundamental things as Euler’s formula: . This lack came to light during physics class, when I was deriving acceleration for something moving in a circle by taking the second derivative of with respect to t. It is so much easier to work with exponential functions than trig functions that it didn’t occur to me that the community college calculus classes would not have covered it.